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Finiteness of Frobenius traces of a de Rham local system

Koji Shimizu

University of California, Berkeley

Friday, December 7, 2018 - 3:35pm to 4:35pm

Vincent Hall 313

Every smooth projective variety over a number field yields a Galois representation via etale cohomology, and the Weil conjecture tells that its Frobenius traces are integers. Fontaine and Mazur conjectured that Galois representations satisfying a local condition (de Rham) arise from geometry and hence have a similar finiteness property. In this talk, I will focus on de Rham local systems on algebraic varieties and explain a finiteness of Frobenius traces follows from the Fontaine-Mazur conjecture for Galois representations and the generalized Riemann Hypothesis